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The sum of Rademacher functions and Hausdorff dimension

Published online by Cambridge University Press:  24 October 2008

Tian-You Hu  and
Ka-Sing Lau
Tian-You Hu
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.
Ka-Sing Lau
Affiliation:
Department of Mathematics and Statistics, University of Pittsburgh, Pittsburgh, PA 15260, U.S.A.
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Abstract

For 0 < α < 1, let for 0 ≤ x < 1, where is the sequence of Rademacher functions. We give a class of fα so that their graphs have Hausdorff dimension 2 − α. The result is closely related to the corresponding unsolved question for the Weierstrass functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 108 , Issue 1 , July 1990 , pp. 97 - 103
Copyright
Copyright © Cambridge Philosophical Society 1990

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References

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